Express your answer as a mixed number simplified to lowest terms. $20\dfrac{1}{3}-13\dfrac{8}{16} = {?}$
Solution: Simplify each fraction. $= {20\dfrac{1}{3}} - {13\dfrac{1}{2}}$ Find a common denominator for the fractions: $= {20\dfrac{2}{6}}-{13\dfrac{3}{6}}$ Convert ${20\dfrac{2}{6}}$ to ${19 + \dfrac{6}{6} + \dfrac{2}{6}}$ So the problem becomes: ${19\dfrac{8}{6}}-{13\dfrac{3}{6}}$ Separate the whole numbers from the fractional parts: $= {19} + {\dfrac{8}{6}} - {13} - {\dfrac{3}{6}}$ Bring the whole numbers together and the fractions together: $= {19} - {13} + {\dfrac{8}{6}} - {\dfrac{3}{6}}$ Subtract the whole numbers: $=6 + {\dfrac{8}{6}} - {\dfrac{3}{6}}$ Subtract the fractions: $= 6+\dfrac{5}{6}$ Combine the whole and fractional parts into a mixed number: $= 6\dfrac{5}{6}$